Chapter 4.7, Problem 27E

To determine

To calculate: Find piecewise function of given graph.

Answer to Problem 27E

The correct answer is $f(x)=\{\begin{array}{l}-\frac{x}{2}+2ifx>0\\ \text{2}xif-\text{2<}x\le 0\\ \text{1 }ifx\ge -2\end{array}$

Explanation of Solution

Given information:In this question graph of defined function is given,all graphs related to straight line equation based,and from basic we know equation of straight line in two point form

  $y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$ where $(x_2,y_2)\&(x_1,y_1)$ lie on straight line.

Calculation: for $f(x)=\frac{-x}{2}\text{+2 }ifx>0$

  $(x_2,y_2)=(2,1)\&(x_1,y_1)=(4,0)$ use equation of straight Line in two form.

  $\begin{array}{l}y-(0)=\frac{1-0}{2-4}(x-4)\\ y=-\frac{1}{2}(x-4)\\ 2y=-x+4\\ y=-\frac{x}{2}+2\end{array}$

Similarly, we can find all rest equation of straight line.

Thus, The correct answer is $f(x)=\{\begin{array}{l}-\frac{x}{2}+2ifx>0\\ \text{2}xif-\text{2<}x\le 0\\ \text{1 }ifx\ge -2\end{array}$